The number of people sleeping rough on the streets has already started to climb. Photograph: Stefan Wermuth/Reuters

Homelessness, that most visceral signifier of hard times, is on the rise and shaping up to be not merely another policy embarrassment for the coalition, but a fully fledged social crisis.

The number of people in England presenting to their local council as homeless rose by 23% in the first three months of this year, compared with the same period in 2010. The numbers of people sleeping rough on the streets has also started to climb.

That 23% figure does not tell the full story: some councils in London – Hackney, Bromley, Islington, Haringey — saw year on year rises in homeless applications of between 80% and 99%.

These statistics, troubling in themselves, are only the first wave. They refer to people, by and large, uprooted by the reverberations of the financial crash of 2008 and the resultant economic downturn.

They do not yet show the impact of public spending cuts which came in on 1 April or housing benefit changes, which will start to be felt from January 2012. When these filter through, the homelessness graph is likely rise dramatically.

This partly explains the terseness of the letter from the Department of Communities and Local Government (CLG) to the prime minister revealed in the Observer . Councils fear the housing benefit cash "savings" to Iain Duncan Smith's Department for Work and Pensions budget is merely "cost shunting" on a grand scale.

One of the most striking revelations in the letter is that the CLG estimates that any savings made in changes to housing benefits – projected to be £270m a year from 2014 – will be swallowed up entirely by the costs of homelessness and temporary accommodation.

Council spending cuts have already laid waste to vital homelessness services, from hostels and day centres to the so-called "floating support" services which help keep vulnerable people in their homes, from teenage parents to victims of domestic violence and people with learning disabilities.

The housing benefit changes and overall benefit cap will exacerbate this. Westminster council, for example, has modelled a scenario showing that 5,000 households, including 4,000 children and hundreds of elderly and disabled people, which are currently renting in the private sector in the borough are receiving housing benefit of more than the proposed £400 a week rent cap.

Hundreds of these families are expected to present themselves as homeless to the council, and if they are formally accepted – current criteria include households with dependent children, pregnant women, people with mental illness — the financial pressure on its budgets will be severe.

The other bombshell in the leaked CLG letter – that the overall benefit caps will make it vastly harder to build affordable new housing for families – is another blow for ministers.

All this is building into a perfect storm for the housing minister, Grant Shapps, who has made tackling homelessness a personal crusade. He set up a Tory homelessness foundation in opposition, and oversees a ministerial working party on homelessness, which is expected to report any day now.

He wrote in the Guardian in January that if he thought the spending cuts were going to increase homelessness and rough sleeping he would not have supported them. The coming crisis will stretch his political credibility to the limit.

Patrick Butler is the Guardian's head of society, health and education